Question

2x – y + 4 = 0 is a diameter of the circle which circumscribed a rectangleABCD. If the co-ordinates of A and B are A(4, 6) and B(1, 9), find the area of rectangle ABCD.

Solution

Correct option is

18 sq. units

 

Since (4, 6) and B(1, 9) do not lie on 2x – y + 4 = 0.

Let M be the mid point of AB then co-ordinates of M is 

   

  

Which passes through P(hk) then

                   

and (hk) lie on 2x – y + 4 = 0

   

Solving (1) and (2), we get

                 h = 1   and   k = 6  

                                    

  

 

SIMILAR QUESTIONS

Q1

 

Find the equation of the circle circumscribing the triangle formed by the lines:

         x + y = 6, 2x + y = 4 and x + 2y = 5,

Without finding the vertices of the triangle.

Q2

Find the equation of the circle circumscribing the quadrilateral formed by the lines in order are 5x + 3y – 9 = 0, x – 3y = 0, 2x – y = 0, x + 4y – 2 = 0 without finding the vertices of quadrilateral.

Q3

Find the equation of a circle which touches the x-axis and the line 4x – 3y+ 4 = 0. Its centre lies in the third quadrant and lies on the line x – y – 1 = 0.

Q4

Find the equations of the circle which passes through the origin and cut off chords of length a from each of the lines y = x and y = –x.

Q5

Determine the radius of the circle, two of whose tangents are the lines 2x+ 3y – 9 = 0 and 4x + 6y + 19 = 0.

Q6

 

Find the equation of the circle which touches the circle

x2 + y2 – 6x + 6y + 17 = 0 externally and to which the lines

x2 – 3xy – 3x + 9y = 0 are normals.

Q7

 

Find the equation of a circle which passes through the point

(2, 0) and whose centre is the limit of the point of intersection of the lines 3x + 5y = 1and (2 + c)x + 5c2y = 1as c → 1.

Q8

Tangents are drawn from (6, 8) to the circle x2 + y2 = r2. Find the radius of the circle such that the areas of the âˆ† formed by tangents and chord of contact is maximum.

Q9

Find the radius of smaller circle which touches the straight line 3x – y = 6 at (1, –3) and also touches the line y = x.

Q10

Let 2x2 + y2 – 3xy = 0 be the equation of a pair of tangents drawn from the origin O to a circle of radius 3 with centre in the first quadrant. If A is one of the points of contact, find the length of OA.